I believe the Americans DID try to conquer Canada in the War of 1812, and I think besieged Quebec, but were beaten back when British reinforcements arrived.

"Conquering Canada" would have been as impossible as the British conquering the United States. The attempt at taking control of part of the St. Lawrence River valley would have been to use it as a bargaining chip in any negotiations, nothing more.

We couldn't do it in 1812 - our resources were not up to the job. By the time of Confederation in 1867, the US didn't need to "conquer" Canada as the US had plenty of land to spread out in, and anyway relations with Britain became more favorable in the decade or so after 1867.

I'm not aware of any invasion plans after 1812, however there were the Alabama claims. This is where the US tried to annex British Columbia, Manitoba and Nova Scotia from the British.

There was War Plan Red in the 1920s, unlikely as that ever was to come about.

It should also be noted that there was a counter strategy on the part of the UK/Canada known as "Defence Scheme No. 1." That called for the occupation of Seattle, Minneapolis and Albany down the Hudson valley.